1. ## word problem

Hi i need help setting up this word problem, this one seams a little more confusing to me.

The dimensions of a gift box are consecutive positive intergers such that the height is the least interger and the length is the greatest interger. If the height is increased by 1cm and the width is increased by 2cm, and the length is increased by 3cm, then a larger box is constructed such that the volume is increased by $\displaystyle 456cm^3$. determine the dimensions of each box.

2. Originally Posted by extraordinarymachine
Hi i need help setting up this word problem, this one seams a little more confusing to me.

The dimensions of a gift box are consecutive positive intergers such that the height is the least interger and the length is the greatest interger. If the height is increased by 1cm and the width is increased by 2cm, and the length is increased by 3cm, then a larger box is constructed such that the volume is increased by $\displaystyle 456cm^3$. determine the dimensions of each box.
For the original box let the height be n

$\displaystyle V_1 = n(n+1)(n+2)$

For the second box add 2 to n , 3 to n+1 and so on

$\displaystyle V_2 = (n+1)(n+1+2)(n+1+2+3) = (n+1)(n+3)(n+6)= 456$

Solve for n which is height - so don't forget to use it to find the other dimensions